The Tropical/Sidereal Debate, Part 2
The Sidereal Point of View
By Kenneth Bowser
The Geocentric World
Late in the first millennium B.C., probably during the lifetime of Hipparchus of Rhodes (mid second century B.C.), the Greeks introduced an innovation in zodiac reckoning that had heretofore been sidereal in the Near East and Eastern Mediterranean world for many centuries: they began to reckon the positions of planets and stars from the northern hemisphere vernal equinox. Until that time the equinox had been described in terms of the degree of the zodiac the Sun traversed when it reached the equinox, variously in the Greek world as 15°, 12°, 10°, 8°, 5° and 3° of Aries as precession slowly changed the Sun’s position in the zodiac at the time of the equinox. This point however, with regard to the modern units employed, is moot because evidence for the use of degrees in extant Greek texts is wanting before the time of Hypsicles (mid-second century B.C.) who was a contemporary of Hipparchus. The Greeks used moonbreadths, cubits and fractions of a circle to measure arc before Hypsicles. The use of 360° base six (sexagesimal) notation is Babylonian. An exception is Meton who was probably exposed to or trained in Babylonian astrology because he described the summer solstice at Athens correctly in terms of the Babylonian zodiac in 432 B.C. Likewise, Eudoxus was probably also exposed to Babylonian reckoning.
During Hipparchus’ lifetime the Sun rose at the northern hemisphere spring equinox with 5° and a fraction of Aries when he was young and 4° and a fraction of Aries when he was old, by sidereal reckoning, the standard of the day. As a careful observer and the foremost astronomer of his era, Hipparchus would have been well aware of these facts. It is unknown if Hipparchus was aware that the northern hemisphere vernal equinox is the southern hemisphere autumnal equinox, in other words, that the northern hemisphere spring is not a global phenomenon. All of Hipparchus’ works are lost but one (his sarcastic commentary on the Phaenomena of Aratus). His achievements are known mainly from Ptolemy’s works, primarily the Syntaxis, a treatise on mathematical astronomy, and the Tetrabiblos, a treatise on astrology.
One may infer from Ptolemy’s works that Hipparchus altered the frame of reference of astronomy and astrology from the reference stars of the Babylonians, who first discerned the zodiac, to make the northern hemisphere vernal equinox begin with the zero degree of Aries. This act represents the break with the old tradition; that is, the coincidence of the zero degree of Aries with respect to Babylonian reckoning did not occur in Hipparchus’ lifetime. One cannot, however, say with surety based on evidential support that Hipparchus actually invented or adopted the tropical zodiac because his use of it does not appear among his extant works. It is an assumption that he did invent it and not an unreasonable one; but one may be on firmer ground to say that if Hipparchus hypothesized the tropical zodiac, Ptolemy made it gospel. One may reasonably ask why it was invented.
The reason is grounded in the idea of the geocentric universe widely embraced in the Greek world. According to this doctrine the Earth is absolutely still with no motion of any kind: no rotation, revolution, precession, nutation, polar wandering or any of the other Earth motions or galactic motion. Geocentric advocates, like their foremost exponent, Claudius Ptolemy, had long held that the Earth was at the center of the universe and every celestial motion was in relation to it. Naturally enough when Hipparchus discovered long-term differences in the positions of stars observed in different eras in relation to the equinoctial points, it was quite reasonable to assume that the stars had actually moved.
That Hipparchus was not absolutely sure of the facts of relative motion (what was moving in relation to what) is obvious from the title to the work upon which his fame is founded, On the Displacement of the Solstitial and Equinoctial Points. If the Earth is motionless the solstitial and equinoctial points cannot be displaced. His positions may have changed over time. Hipparchus probably embraced the scientific method according to which the question, “How do you know?” is never out of bounds. But the supposedly free-thinking Greeks sometimes made life difficult for people whose flights of fancy strayed too far from orthodoxy, mainly because the Greeks let philosophers meddle in matters beyond their purview. For example Philolaus (480-385 B.C.) was ridiculed by Aristotle for proposing that the Earth revolves around a central fire; Heraclides Ponticus (387-312 B.C.) was ridiculed even many centuries later by Simplicius for proposing that the Earth rotates on its axis; and especially Aristarchus (310-230 B.C.) who proposed that the Earth orbits the Sun (the original heliocentric theory) was threatened by Cleanthes with indictment for impiety because the heliocentric theory was contrary to Platonic thought. An indictment of impiety that led directly to his demise was also brought against Socrates in consequence of his independence of thought. Aristarchus even proposed that the Sun and the stars are fixed and that the Earth moves with respect to those fixed positions. Aristarchus’ configuration is remarkably close to the truth, but he was too far ahead of his time. His heliocentric theory was not embraced in the ancient world and did not completely displace the geocentric theory until nearly two millennia after his death.
The pressure against Aristarchus was brought by the arbiters of the then conventional wisdom who “knew better” in the same way that everybody “knew” for millennia that the world was flat. Once presented with compelling evidence that it was actually spherical (first proposed by Pythagoras), they subsequently “knew” that it was motionless and the center of the universe. These ideas dragged on for centuries mainly due to the combined influence of Aristotle and Ptolemy. Martin Luther (1483-1546), like many other intellectuals of his day, savaged Nicholas Copernicus (1473-1543) in the middle of the sixteenth century for advancing the heliocentric theory that places the Sun in the center of the solar system and puts the Earth in motion around it. All of this bogus “knowing” masquerading as knowledge depends on the logical fallacy known as, “an appeal to authority” (argumentum ad verecundiam—[an argument to respect]). In other words, “Such and such is true because everybody says so.” Stereotypes that fly in the face of archetypes are usually based on appeals to authority.
The weight of orthodoxy may not have impressed itself on Hipparchus; perhaps his position on the island of Rhodes was secure and he felt free to speculate; but an argument from silence proves nothing. It is obvious, however, that if the stars are perceived to slowly move over long periods of time, one can only see that in relation to a fixed standard or a much slower changing standard. Without such a standard, era-to-era comparisons would be meaningless. Unless it could be established what was moving and what was fixed in space, the issue of foreground and background would always be confounding.
The need for a fixed standard is one of the twin pillars that supported tropical reckoning; the other pillar rested on the evidence of one’s eyes that could not be argued: the spring equinox very nearly coincided with the zero degree of sidereal Aries during Ptolemy’s lifetime. That is, one could see the Sun rising due east at dawn on the day of the northern hemisphere spring equinox with the earliest part of the constellation Aries in Ptolemy’s day, and close to the beginning of Aries for a long time afterward. Refraction and the Sun’s glare made any naked eye approximation too difficult to argue for two hundred years after the Age of Pisces began in A.D. 221 with respect to the zodia noeta (equal length signs thirty degrees in extent).
By the fifth century of the Christian Era the curtain had all but completely fallen on Late Antiquity as a sophisticated period in the West. As the Dark Age settled over the West and tropical and sidereal reckoning began to diverge, there was almost beyond question nobody in the West who understood what was happening nor why. The divergence may not even have been noticed since the record of observations in the West during the Dark Age is abysmal. If anybody noticed, understood and wrote about what was happening, such a treatise did not survive or has not yet been discovered. The Arabs and the Indians noted the divergence but not its cause. Dark Age Europeans demonstrated no awareness of astronomical/astrological sophistication except for the minuscule number who had access to and could read Ptolemy’s Almagest or his Handy Tables or Theon’s Handy Tables that were all written in Greek. Yet this extremely small group also could not have understood why the sky was different than what Ptolemy wrote about it from his own work.
Tromp L’Oeil: How the Tropical Zodiac Appears Fixed But Is Not
It is ironic that Ptolemy’s efforts to institutionalize the tropical zodiac, to make it a fixed standard tied to the geodesy of what he asserted was a fixed Earth, made it a permanently changing standard. That is an inevitable fact because the Sun is the center of the solar system which puts the Earth in motion in several long and short term modes. Possibly Hipparchus but definitely Ptolemy got it backwards. The equinox moves very fast in relation to the star field, not the other way around.
For example, the sidereal zodiac is bisected by two first magnitude stars close to the ecliptic, Aldebaran in the center of Taurus and Antares in the center of Scorpio. The tropical position of Antares, the brightest star in Scorpio, was 1° 23' 12.95" greater on January 1, 2001 than it was on January 1, 1901. That may not seem like a large difference, but it is equivalent to 4,992.95 seconds of arc; yet the star didn’t move that much with respect to the Earth. The star appeared to move that much with respect to the Earth but what actually happened is that the equinox moved that much with respect to the star. The tropical frame of reference is constantly in motion with respect to the sky because that system is tied to the vernal equinox instead of the sky. Whether or not the equinox moves is no longer a point at issue. Copernicus showed indirectly that it moves in 1543 with the publication of his De Revolutionibus Orbium Coelestium. Galileo also showed indirectly that the equinox moves in 1610 with the publication of his Siderius Nuncius. With the publication of Isaac Newton’s Principia in 1686 and 1687 the matter of what is moving in relation to what is fixed was explicitly settled and no longer a point that could be argued, except in astrological circles. Significantly the seventeenth century was also when astrology was being dropped everywhere from university curricula. What had finally been proven was that the geocentric model is without merit. The vernal equinox is not fixed in space as Ptolemy maintained as an absolute incontrovertible fact.
In terms of fixed sidereal reckoning, the proper motion of Antares during the twentieth century—how much it actually moved in 100 years with respect to the Earth—was 2.15 seconds of arc. That bears repeating: Antares moved 2.15 seconds of arc in terms of sidereal reckoning in 100 years versus 4992.95 seconds of arc in terms of tropical reckoning in 100 years. The smaller number is .00043 of the larger one or consider that 4992.95 is more than two-thousand, three-hundred and twenty times greater than 2.15. The human eye cannot detect an arc of only 2.15 seconds or anything close to it. This is the essential difference between tropical and sidereal reckoning: the tropical zodiac is moving with respect to the stars and the sidereal zodiac is essentially fixed with respect to those same stars. There are 60 seconds per minute of arc and sixty minutes per degree, thus 3600 seconds of arc per degree. At the rate of 2.15 seconds per century, it will take Antares 167,000 years to move one degree from the vantage-point of the Earth. That is 1,670 centuries. The stars are going nowhere fast, but since the advent of writing five millennia ago that invoked the historical era at Sumer in Mesopotamia and pre-dynastic Egypt, the equinoxes have moved seventy degrees with respect to the stars for the same civil date. Half of the Age of Taurus, all of the Age of Aries and most of the Age of Pisces have passed by since then.
Antares is typical of the actual motions of stars as seen from the Earth. Some are faster; some are slower but as a practical matter they are fixed. The night sky looks today just as it did when Egypt became a federated state in the third millennium B.C. Tropical reckoning is fixed with respect to the equinox but the equinox moves with respect to the stars, yet the logic of tropical reckoning that stops at the zero degree of Aries requires the opposite to be true. That is, tropical reckoning requires that the sky moves with respect to a fixed earth; but the appearance is not the reality. The geocentric system is not simply a way of looking at things. It puts the cart before the horse. The solar system is heliocentric. The Sun is at the center of the system and all other bodies in our solar system move around it and not the Earth. The equinoxes and the stars are not simply moving in relation to each other. To maintain as much equates a local and misleading point of view with an overarching one. If Antares were locked up in a glacier and thus, strictly speaking, in motion at a glacial speed, the equinox would streak past it at a speed greater than Mach 3 in comparison. So while it is true that the sidereal zodiac is not absolutely fixed, except to an epoch and a star, it is a fatuous argument to maintain that both sidereal and tropical reckoning are simply in motion because the equinox moves proportionally faster than a bullet against what for all practical purposes is a fixed sky.
How Precession Works
The mechanism of precession cannot be understood from a geocentric point of view. What is actually happening in the Sun-Earth relationship can only be understood when the facts are laid out in the astronomically correct heliocentric system.
Hipparchus is credited with discovering precession of the equinoxes but he couldn’t have fully appreciated what he had found for lack of sufficient background information. Precession of the equinoxes is the westward movement of the equinoxes with respect to the stars at the rate of approximately 50.27" per year (in 1975). It is caused by the attraction of the Sun and Moon to the Earth’s equatorial bulge. Any non-rigid or semi-rigid rotating body (like the Earth) tends to accumulate material around its equator. Accordingly the Earth’s polar diameter is twenty-seven miles less than its equatorial diameter. The gravitational couples between the Sun and the Earth and the Moon and the Earth are not spread evenly over the planet because of this bulging equator that gets most of the attractive force. The equatorial bulge is especially significant because the Earth’s spin axis is not perpendicular to the plane of its orbit, but inclined to it by nearly 23.5° (although that value varies between approximately 22.1° and 24.5° with a period of 41,000 years). The Sun-Moon attraction to the equatorial bulge tends to pull the Earth upright such that its spin axis would be perpendicular to the plane of its orbit if the Earth didn’t resist the attractive force through the agency of its rotation. What this resistance feels like can be appreciated by holding a spinning gyroscope in your hand. If you rotate your wrist while holding the spinning gyroscope, you can feel resistance to the change in orientation in space of the gyroscope’s spin axis. This is directly analogous to what happens to the Earth.
If a torque (a twisting force) is applied to a rotating body, the body will respond at a right angle to the vector (a line of force) of the applied torque. What that looks like is illustrated by a child’s spinning top that wobbles: the instantaneous spin axis of the top will precess. Stated somewhat differently, the effect of gravity on the low point in the spin of a hypothetical top is to pull the low point down to the surface on which the top spins so that the top falls over. The top resists being pulled down to that surface through the agency of its spin but its spin axis moves in a direction that is ninety degrees to the force of the gravitational tug on the low point in its orbit. In the same way on a bigger scale, the primary torques acting on the Earth are the gravitational attractions of the Sun and the Moon. The inertial energy in the Earth’s rotation is great enough to resist the gravitational force that would quickly change its orientation in space if it were not spinning. The Earth is affected nonetheless by the gravitational force exerted on its equatorial bulge and responds at a right angle to the applied force, i.e., its spin axis precesses, but very slowly. The image of a child’s toy (a wobbling top) has to be slowed down into extreme ultra slow motion. The forces, masses and distances in the three way relationship between the Sun, the Moon and the Earth are so huge that it takes 25,800 years to complete a single wobble cycle. During that time the celestial pole, which is the terrestrial pole extended out into space, will describe a circle with a radius of 23½°. That means that Polaris, currently the pole star, occupies that position only temporarily. Twelve thousand years from now, Vega, the alpha star in the constellation Lyra, will be the pole star. That changes the orientation of the equinox with respect to the ecliptic by thirty degrees every twenty-one and a half centuries which accounts for the astrological ages.
In the total scheme of things all stars that are more than 23½° from the ecliptic poles will successively occupy every second of right ascension, which is a tropical coordinate, in the course of 25,800 years. The declinations of the stars will vary through 47° (2 x 23½) every 12,900 years. That means that the dates and local times when stars rise, culminate and set for most locales on the planet slowly but continuously change over time from the civil dates and local times at which they currently rise, culminate and set. Both the x and the y axes of the equatorial system (the right ascension and declination system) change continuously but only the x axis of the ecliptic system (celestial latitude and celestial longitude) changes because the equinox is in motion along the ecliptic. Only the proper motion of a star in celestial latitude can change that coordinate.
Both features of tropical reckoning that may have seemed secure in Ptolemy’s day—a fixed standard of measurement and visual confirmation of the confluence of the Sun, the beginning of Aries and the northern hemisphere spring equinox—were quickly demolished. It has taken, however, almost two millennia for that to be understood and then entertained in astrological circles in the West. The equinox moves fast in relation to the sky and a careful observer would have seen the Sun rising in Pisces at the time of the equinox shortly after the opening of the Piscean Age as the Arabs and the Indians clearly did see it in the latter part of the first millennium A.D.
There is a persistent question in the tropical-sidereal debate about the matter of the rising times of the tropical and sidereal signs that has been offered as evidence of the invariability and the possible use of the tropical zodiac by the Babylonians. The rising times of the tropical signs are little changed over several millennia but they do change more substantially over longer periods as the Earth’s orbital eccentricity and the obliquity of the ecliptic wax and wane. These change the dates of the solstices, equinoxes, aphelion, perihelion, the lengths of the seasons and the tropical rising times.
The rising times of the sidereal signs change because the rising time of any star that can rise (i.e. that is not circumpolar) is a function of the latitude of the place in question and the declination of the star in question. Since declination is a tropical coordinate and subject to precession, the rising times of stars must change as precession in declination changes. The rising time issue is therefore a circular argument (which is like saying that the rising times change because they change [sic]) except in one special case: at the equinoxes when all bodies rise rightly rather than obliquely and their declinations are not a factor. The rising times of the tropical signs are essentially static (in the short term astronomically speaking) because they have no relation to stars. Therefore if the sidereal rising times of signs reckoned from the fixed stars change because the orbital characteristics of the Earth make it move in relation to the stars, it is once more merely an appearance that the vernal equinox is fixed. The celestial pole of the Earth precesses. The celestial equator is perpendicular to the pole. They are parts of the same whole (the Earth). When the pole moves, the equator and the equinox move with it. There is no way around that. The argument appears to be valid because the tropical rising times at the equinox change quite slowly, but the sidereal rising times change because the Earth is wobbling on its spin axis and fast in astronomical terms, not because the stars are actually moving above a fixed Earth. The tail does not wag the dog.
The Babylonians were careful to take into account where the beginning of Aries actually was in relation to the equinox. That is abundantly clear from the corrections they applied to the rising times and in particular to the demonstrable fact that the rising times pertain to a sidereal and not a tropical schema. The rising time argument in favor of the constancy of the tropical zodiac cannot trump or somehow obviate that the equinox moves against the field of stars. It is in no way comparable to the overwhelming reality of the total demolition of the geocentric hypothesis by the heliocentric facts. The tropical rising time argument appears to be valid until it is seen as a form of the artistic device known as trompe l’oeil (to deceive the eye) in that the equinox appears to be fixed in time but once more, it is an appearance that cannot contravene precession.
Once one grasps what is moving in relation to what is fixed, the slowly changing rising times of the tropical zodiac can easily be seen as a vestige of an antiquated system that is based on the constant effort of astronomers in the ancient world “to save the appearances,” i.e., to account for observed phenomena. If a model could do that it was invested with merit whether the model was correct or not. But as every undergraduate knows who has taken his first class in logic, a valid argument is not necessarily true. This is no semantic trick. A valid argument that is not simultaneously true leads to false conclusions. The use of epicycles and deferents employed by Ptolemy was a very impressive achievement for his time because it could describe reality fairly well by the looser standards of the ancient world. Ptolemy’s model was flawed, however, and has been totally abandoned because it doesn’t describe reality nearly as well as the true facts do. The planets don’t move in perfectly circular epicyclic orbits around the Earth. The planets move in elliptical orbits around the Sun. The epicycle/geocentric universe model is valid but it isn’t true. The rising time argument also appears to be valid but it isn’t true. The rising time issue is due primarily to the obliquity of the ecliptic. Equal arcs of the equator and the ecliptic do not pass through the meridian or the horizon in equal spans of time except at the equinoxes. The attempt is made with the tropical rising time argument to make that exception trump the much bigger issue of precession by ignoring that the equator is connected to the pole.
The Function of the Equinox
The equinox appears throughout Babylonian material but not as a consideration invested with astrological merit (because there are no stars that stay conjoined to the equinox over time), rather as an astronomical one that facilitated the determination of terrestrial latitude (before the latitude/longitude grid came into general use), timekeeping and the intercalation of extra lunar months to keep the calendar synchronized with the solar year. The tropical rising times are merely a device to facilitate some computations. The equinox is a useful point of reference for measuring arc lengths. Yet use of the equinox to note the day when days and nights are of equal duration and as part of the computation to note the ratio between the longest and shortest days has nothing to do with the zodiac. To equate the zodiac with the northern hemisphere seasons is to confuse the zodiac with the seasons; they are not the same. The Babylonians never equated the seasons with the zodiac.
The Babylonians generally computed the equinox in astrological work but only approximately. It was rarely observed which was explicitly stated by scribes who recorded astrological material. Most Babylonian horoscopes even show the nearest solstice or equinox but if any astrological influence was attributed to the equinoctial points, it was not recorded thus no argument can be plausibly construed about their use of the equinox beyond what they did say about it. The Babylonians did, however, attribute influence to both the celestial longitude and latitude of bodies, a practice still embraced by Eastern and Western siderealists. The Babylonians took into account the anomaly of the Moon; they determined the length of the sidereal month, they recorded the length of the synodic month correct to the fourth decimal place; they predicted eclipses and heliacal phenomena; individual stars received special attention; the duration between sunset and moonset, sunrise and moonrise was recorded which helped them construct their cinematic model of the sky. The Babylonians overlooked nothing of importance.
They had nothing to say about the equinox or tropical signs because there were no tropical signs until very late in the first millennium. Yet an argument from silence has been advanced in some circles that attempts to “prove a negative” to impose the tropical zodiac on the Babylonians. That is, the point is sometimes pressed that because the equinox appears frequently in cuneiform records that one cannot dismiss the tropical zodiac as a possibility among the Babylonians. It is always hard to disprove a negative proposition, which can be taken to absurd extremes in order to keep concocted ideas alive. For example, it is impossible to say absolutely, incontrovertibly that the Easter bunny does not exist especially when one sees advertisements and cardboard cut-outs of him every year around the time of the northern hemisphere vernal equinox. The Babylonian use of the equinox is just such a cardboard bunny, but there is no evidence that the Babylonians thought the bunny sprang to life, as it were, and was hiding just out of sight. The equinox was a marker that was used to coordinate agricultural activities, geodesy and tell time — as it was for Hesiod — not an astrological idea invested with meaning.
Why the Babylonians Are Celebrated
The Babylonians developed the first mathematical model that could accurately predict future positions of the Sun, Moon and planets, a staggering achievement for the first millennium B.C., hailed by historians of science as one of the great technical triumphs of Antiquity. The Greek model was merely explanatory; it was not predictive until Hipparchus in the second century B.C. adapted Babylonian parameters to the scheme of epicycles and deferents developed by Apollonius of Perga (c. 242 B.C. – c. 190 B.C.) that was much used later by Ptolemy. The Greeks benefited enormously from Babylonian knowledge and skill, adopting wholesale Babylonian astronomical and astrological parameters, especially the zodiac, which were the labor of centuries in Mesopotamia, into Greek astronomy and astrology. Hipparchus freely acknowledged his debt to Babylon, according to Ptolemy.
Babylonian priority with respect to the zodiac is their supreme achievement. Ephemerides rank next in importance. All Babylonian astrology, ephemerides, procedure texts and the cinematic model of the sky are in relation to the sidereal zodiac. Babylonian ephemerides are based on many centuries of observations and a brilliant innovation called period relations by modern scholars. Period relations are a combination of sidereal periods and synodic periods. A sidereal period is the time that a planet requires to orbit the Sun as seen from the Earth. A synodic period is the elapsed time between successive conjunctions of a planet with the Sun as seen from the Earth. The sidereal period of Jupiter, for example, is 11.86223 years. The synodic period for Jupiter is 398.88 days. Jupiter’s synodic and sidereal periods coincide at intervals of 427 years. That is, 36 revolutions of the planet and 391 synodic periods are both completed in 427 years. That means Jupiter returns to the same positions in the zodiac very closely every 427 years with respect to its synodic phenomena, both in terms of order of appearance and interval in time. A planet’s synodic phenomena are its first appearance (visibility), first stationary point, opposition (to the Sun), second stationary point and last appearance (visibility).
Period relations are as effective now as they were three thousand years ago. In 2011 Jupiter turned stationary retrograde on August 30 at 15° Aries 27° and stationary direct on December 25 at 5° Aries 27°. Four hundred twenty-seven years ago in 1584 Jupiter turned stationary retrograde on August 26 at 16° Aries 31° and stationary direct on December 21 at 6° Aries 31°. In this particular sequence the difference in positions amounts to four days and 1° 04°. The agreement in some Jupiter period relation sequences differs by a single day and less than a quarter of a degree. There are 155, 958 days in 427 years. The agreement between 1584 and 2011 is close enough to allow someone with a record of long-term observations to predict the positions of Jupiter in 2011 by comparing that year to 1584.
Only the Babylonians had the observational data in the ancient world to figure out period relations. Moreover, period relations make no sense in a tropical context unless one uses fractions of the periods in order to make the tropical error due to precession smaller. The problem is most obvious with a large period relation like Jupiter’s. In 427 years the difference between tropical and sidereal reckoning is nearly six degrees. That means that tropical reckoning cannot yield accurate long-term positions of bodies, without adopting sidereal parameters, since tropical reckoning gets out of sync with the sky by thirty degrees in twenty-one and a half centuries. The period relations of the other planets with shorter periods display the same type of behavior that is equally close. The epicycle, deferent and equant model used by Ptolemy is far from exact and was found to be wanting in respect of accuracy by the time of Johannes Müller (1436-1476), known to astrologers as Regiomontanus. Furthermore, while the epicycle model can predict retrogradation, it only approximately reflects the movement of the planets because they do not move in epicycles around the Earth. Moreover their orbits are not circular as Plato insisted that they had to be, rather ellipses. The Babylonians did not impose philosophy on the sky. They did not insist on a geometric model of the sky. But what they had not only worked, it did not compromise astronomical facts. The Babylonians hitched their wagon to a star, so to speak, to something real.
The Evidence for Tropical Reckoning
The most exhaustive compendium of early tropical astrology is the Catalogus Codicum Astrologorum Graecorum (Catalog of the Codices of the Greek Astrologers). Known by its acronym, the CCAG is a large work published in twelve volumes between 1898 and 1953. Most of it is written in Greek and Latin. The early history of tropical astrology is unreliable regarding both the quality of the information and their dates which is clearly shown by the scraps, fragments and legends that were gathered together to form the earliest part of tropical astrology. Franz Cumont (1868-1947), the scholar who was the driving force behind the CCAG described the early period as “apocryphal works of a mythical antiquity.” He was right to describe it that way because, to date, there is still no evidential support for what is claimed for the early period.
One of the earliest accounts is of a Babylonian priest/astrologer by the name of Berosus who supposedly came to the Greek island of Kos circa 275. B.C. to dispense astrological wisdom to the Greeks. There is another claim that around the year 150 B.C. an Egyptian pharaoh, Nechepso (Necho II?) and his priest/advisor Petosiris, wrote treatises or became known for their astrological acumen but there are no horoscopes or actual works that can be directly attributed to them, if they indeed existed. As with Berosus, there are many references to them but in the absence of hard evidence, one cannot know if their legends are grounded in fact. The legend surrounding Hermes Trismegistus (thrice greatest Hermes — the Egyptian god Thoth [Mercury]) from the same period is enormous. He was another figure who supposedly dispensed wisdom to then contemporaneous Greeks and Egyptians about astrology, but at present it is not known what was dispensed, to whom, when or if any real person or persons is behind the legend of Hermes. Greek astrological works from the first five centuries of the current era are much more complete and sure with respect to date as the CCAG shows. The state of tropical astrology during the Hellenistic Period however, is legendary and unsubstantiated. This condition is underscored by a remarkable fact:
“It is worth noting that Ptolemy does not cite any planetary observations by Hipparchus, or for that matter, any such observations between the end of the 3rd century and shortly before his own time.”
Astrology has always been based on astronomical considerations, even if some of them were not well understood. Unless they were lost, burned or stolen, the dearth of material is amazing. One must wonder, if tropical astrology were well underway during the Hellenistic Period, why there is no record of astronomical work to go with it as there always was among the Babylonians.
In stark contrast to the meager state of tropical astrology during the Hellenistic Period, Babylonian sidereal astrology was at its height during the same period, which is largely unknown in the West. An example of the accuracy of Babylonian positional astronomy during the Hellenistic Period is a table of New Moons that covered the period 104 B.C. to 101 B.C. This table covered the anomalistic month (perigee to perigee) and gave the latitude and longitude of the Moon, the date and time of the first appearance of the crescent Moon and the date and time of the New Moon. For the New Moon of March 23, 104 B.C., the text gives 4:11 a.m. LMT in terms of modern reckoning. Modern computation gives 2:46 a.m. LMT.
Conjunctions of the Sun and Moon are not visible because the Moon is too close to the Sun to be seen, therefore a Sun-Moon conjunction must of necessity be computed. A time difference of one hour and twenty-five minutes is less than a degree of arc, which is extraordinary accuracy for the era and far better than any Greek effort extant for the first or second centuries B.C. According to Professor emeritus Asger Aaboe of Yale University who translated it, the text was entirely computed, not observed. Furthermore there is a large body of hard evidence that sidereal astrology was practiced in Roman controlled Egypt. The Egyptian horoscopes were reckoned from a sidereal ecliptical tradition, whereas earlier Egyptian astrology is mostly reckoned from the equator, not the ecliptic. Horoscopes from the Greek colony, Oxyrhynchus in Egypt, which used mostly Babylonian parameters, are significantly more accurate than then contemporary tropical astrology. The Oxyrhynchus horoscopes are almost uniformly sidereal into the sixth century A.D. when the record ends. All of these facts strike at the heart of alleged Greek priority in astrology and demonstrate the widespread use of the sidereal zodiac in the ancient world. The astrologers at Oxyrhynchus may also have been the ancestors of the legendary figures from the second and third centuries B.C. if they existed at all. That is far more likely than that Nechepso, Petosiris and Hermes had any connection with tropical astrology.
Tropical Reckoning Compared to Sidereal
The oldest Greek horoscope from a literary source dates from 72 B.C., although its positions correspond very poorly to the date for which it is supposedly computed. In fairness, other early Greek horoscopes from Alexandria, Rome and elsewhere around the Mediterranean, have positions that are only wrong by a few degrees, although they are often wrong by as much as five degrees when degrees are shown. If tropical astrology were well established in the Hellenistic Period, one must wonder why the oldest extant example of a Greek calendrical horoscope is as recent as 62 B.C. It is a stone monument, never completed, to a monarch (Antiochus I of Commagene ) who ruled a part of what is now Turkey. Otto Neugebauer in 1958 determined the date from the horoscope with some difficulty because the position of one of the planets is incorrect: Jupiter was well into Cancer tropically and sidereally, but it was rendered in Leo. In addition the Sun, Venus and Saturn were omitted. It’s hard to know just what Antiochus’ Hierothesion actually represents. It is not sidereal and its Jupiter position doesn’t make sense if the vernal equinox = 0 degrees Aries standard was in place then.
The earliest known Greek horoscope on papyrus dates from 10 B.C. The earliest extant example of sidereal astrology for an individual is precisely four hundred years older, i.e. from 410 B.C. Some have objected that because the 410 B.C. horoscope doesn’t have degrees, only signs, that it could be tropical but the Greeks hadn’t adopted degrees from the Babylonians that early. Hipparchus, a second century B.C. figure, probably converted early Greek units of measure into degrees, according to Goldstein and Bowen, including the work of Timocharis. The authority of Cleostratus who is alleged to have introduced the zodiac into Greece in the sixth century B.C. has long been discounted for lack of evidence. That the pre-Hellenistic Greeks did use the constellations extensively is not contested; but if there is any credible evidence extant that the 0 degrees Aries = vernal equinox standard was employed in the fifth century B.C., there needs to be hard evidential support for it. Certainly the rising time argument cannot be construed as evidence because it requires the inference that the use of an equinox means “tropical” whereas Hesiod and the Babylonian material contravene that assumption; moreover there are no horoscopes or any kind of text advanced to date to support the assertion that tropical zodiac reckoning was in place in the fifth century B.C. Thus it is unlikely in the extreme that the 410 B.C. horoscope could be Greek.
The lives of Hipparchus and Ptolemy were separated by three hundred years. Where then is the tropical astrology from the Hellenistic Period if indeed it had reached a state of development during that period but for which there is almost no evidence? The evidence for tropical astrology does not appear to any significant degree, by any measure, until the Roman Imperial Period, not the Hellenistic period. This is interesting in view of the high state of development of Babylonian planetary and lunar theory, as early as the fifth century B.C., their discovery and long-time use of the zodiac, their development and use of accurate ephemerides and hard evidence for the use of astrology many centuries before the Greeks can produce evidence of their use of it.
The Greeks unquestionably came late to astrology, with a massive debt to Babylon, yet the Greeks get most of the credit for modern astrology. Appreciation of the Babylonian place in astrology is only well known among academics, although lack of recognition in the modern astrological community is not the main issue in the tropical-sidereal debate. The most important and fundamental issue to siderealists everywhere is that the Greeks adopted the zodiac from the Babylonians and then arbitrarily changed the fiducial, or point of reference, from the stars to the equinox. Whether then contemporary Western astrologers understood the change is not the issue. Few astrologers know this; they assume that Western astrology really begins with the Greeks and that the northern hemisphere vernal equinox has always been the standard for reckoning celestial longitude. That is not true. The zodiac was originally reckoned from the stars, not the northern hemisphere seasons and for one billion two hundred million Indians, a few thousand Westerners in the United States and Europe presently, and the whole of the ancient world until the Greeks, the stars were the only standard.
In less than four hundred years tropical reckoning will be fully thirty degrees removed from the Babylonian marking stars that are the antecedents that define the zodiac still. In 11,000 years the tropical zodiac will be completely upside down with respect to its namesake stars. The difference between tropical and sidereal reckoning is so great even now — almost twenty-five degrees — that the matter cannot be put off any longer and needs to be re-examined by a new generation.
I wrote down a spirited exchange I had with the renowned twentieth century astrologer, Dane Rudhyar in September 1976 at Sunnyvale, California. I asked him why he and Cyril Fagan had not been able to sit down and talk about the tropical – sidereal controversy. His sharp reply surprised me. He said, “What Fagan never understood was that astrology changed as men changed.” It was obvious to me at that moment that Rudhyar saw astrology as an anthropomorphic projection and thus subject to revision. The Babylonians, on the other hand, definitely saw astrology as divination by the sky and thus immutable.
Excerpted from An Introduction to Western Sidereal Astrology, by Kenneth Bowser. Reprinted with permission by The American Federation of Astrologers. © 2012 Kenneth Bowser. All rights reserved.